Finite Group Databasebeta

← #37544830

Subgroups — #37544830

Order 23168.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041900C211yesmaximal, characteristic, complemented
2#26041671C211yesmaximal, characteristic, complemented
3#26041661C211yesmaximal, characteristic, complemented
4#26041638C211yesmaximal, characteristic, complemented
5#26041629C211yesmaximal, characteristic, complemented
6#26041498C211yesmaximal, characteristic, complemented
7#26041491C211yesmaximal, characteristic, complemented
8#26041486C211yesmaximal, characteristic, complemented
9#26041481C211yesmaximal, characteristic, complemented
10#26041441C211yesmaximal, characteristic, complemented
11#26041435C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic
13#26041418C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#536×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×#15668436C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24#19153816C2211yescharacteristic
25#19153811—21no—
26#19153804C2211yescharacteristic
27#19153802—21no—
28#19153798—21no—
29#19153795C2211yescharacteristic
30#19153794—21no—
31#19153790C2211yescharacteristic
32C4×Dic362C2211yescharacteristic
33C4×D724C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35C4⋊#13089678C2211yescharacteristic
36#19153740C2211yescharacteristic
37#19153740C2211yescharacteristic
38#19153740C2211yescharacteristic
39#19153740C2211yescharacteristic
40#19153740C2211yescharacteristic
41#19153740C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48C2×#41×C181C2211yescharacteristic
49C22×Q8×C181C2211yescharacteristic
50C4⋊Q8×C181C2211yescharacteristic
51C4⋊Q8×C181C2211yescharacteristic
52#124×C181C2211yescharacteristic
53#124×C181C2211yescharacteristic
54#123×C181—21no—
55#123×C181—21no—
56C22⋊Q8×C181—21no—
57C22⋊Q8×C181—21no—
58#117×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C4×D181—21no—
64#15668439—41no—
65#15668439—41no—
66#15668439—41no—
67#15668437—41no—
68#15668436—41no—
69#15668436—41no—
70#15668436—41no—
71#15668434—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81C22⋊Dic181—21no—
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86C4×Dic181—21no—
87#41×C181—41no—
88#41×C181—41no—
89C2×Q8×C181—21no—
90C2×Q8×C181—41no—
91C2×Q8×C181—41no—
92C2×Q8×C181C2311yescharacteristic
93C2×Q8×C181C2311yescharacteristic
94C2×Q8×C181C2311yescharacteristic
95C2×D4×C181—21no—
96C2×D4×C181C2311yescharacteristic
97C22×C4×C181—21no—
98C22×C4×C181—21no—
99C22×C4×C181C2311yescharacteristic
100C4⋊C4×C181—21no—
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181—21no—
104C4⋊C4×C181D411yescharacteristic
105C4⋊C4×C181D411yescharacteristic
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C22⋊C4×C181D411yescharacteristic
111C22⋊C4×C181D411yescharacteristic
112C42×C181C2311yescharacteristic
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—81no—
118D724—21no—
119D724—21no—
120C22⋊D181—81no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C4×D181—81no—
125#13089678—21no—
126#13089678—21no—
127#13089678—21no—
128#13089678—21no—
129C23×C181—21no—
130C23×C181C2×D411yescharacteristic
131Q8×C181—21no—
132Q8×C181—21no—
133Q8×C181—21no—
134Q8×C181—21no—
135Q8×C181—21no—
136Q8×C181—21no—
137Q8×C181—42no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—42no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—42no—
147C2×C4×C181—42no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2411yescharacteristic
154C22×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181C22×D411yescharacteristic
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—21no—
168C4×C181—21no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181H(5,𝔽2)11yescharacteristic
173C4×C181H(5,𝔽2)11yescharacteristic
174Dic181—41no—
175Dic181—41no—
176Dic181—41no—
177C2×C181—41no—
178C2×C181—81no—
179C2×C181#53511yescharacteristic
180C2×C181#57711yescharacteristic
181C2×C181#57811yescharacteristic
182D181—81no—
183C181#322511yescharacteristic, complemented, Sylow
184#3225—1811nomaximal, Sylow
185#542—1811no—
186#536D18111yescharacteristic, complemented
187#497—1811no—
188#495—1811no—
189#489—1811no—
190#487—1811no—
191#464—1811no—
192#463—1811no—
193#462—1811no—
194#461—1811no—
195#452—1811no—
196#451—1811no—
197#449—1811no—
198#448—1811no—
199#433—1811no—
200C2×#41C2×D18111yescharacteristic
201C22×Q8C2×D18111yescharacteristic
202C2×Q16—1811no—
203C2×Q16—1811no—
204C2×Q16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×D8—1811no—
210C4⋊Q8—1811no—
211C4⋊Q8C2×D18111yescharacteristic
212C4⋊Q8C2×D18111yescharacteristic
213#126—3621no—
214#124—3621no—
215#124—1811no—
216#124C2×D18111yescharacteristic
217#124C2×D18111yescharacteristic
218#123—21no—
219#123—21no—
220#123—3621no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—3621no—
224C22⋊Q8—1811no—
225#121—1811no—
226C4×Q8—1811no—
227C4×D4—1811no—
228#117C2×D18111yescharacteristic
229C4⋊C8—1811no—
230C4⋊C8—1811no—
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#103—1811no—
237#102—1811no—
238#102—1811no—
239C22⋊C8—1811no—
240C22⋊C8—1811no—
241#97—1811no—
242C4×C8—1811no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—3621no—
249C2×Q8—1811no—
250C2×Q8C22×D18111yescharacteristic
251C2×Q8C22×D18111yescharacteristic
252C2×Q8C22×D18111yescharacteristic
253C2×D4—21no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4C22×D18111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—3621no—
260C22×C4C22×D18111yescharacteristic
261Q16—7241no—
262Q16—7241no—
263Q16—7241no—
264SD16—7241no—
265SD16—7241no—
266SD16—7241no—
267SD16—7241no—
268D8—7241no—
269C2×C8—1811no—
270C2×C8—1811no—
271C2×C8—1811no—
272C2×C8—1811no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4C22⋊D18111yescharacteristic
283C4⋊C4C22⋊D18111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4C22⋊D18111yescharacteristic
294C22⋊C4C22⋊D18111yescharacteristic
295C42—3621no—
296C42C22×D18111yescharacteristic
297C42C22×D18111yescharacteristic
298C23—21no—
299C23—3621no—
300C23C2×C22⋊D18111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—3621no—
309Q8—3621no—
310Q8—14481no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—3621no—
315D4—3621no—
316D4—14481no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—3621no—
327C2×C4—14481no—
328C2×C4C2×C22⋊D18111yescharacteristic
329C2×C4C2×C22⋊D18111yescharacteristic
330C2×C4C2×C22⋊D18111yescharacteristic
331C2×C4C2×C22⋊D18111yescharacteristic
332C2×C4C2×C22⋊D18111yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—3621no—
335C8—3621no—
336C8—3621no—
337C8—3621no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22C22×C22⋊D18111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—7241no—
357C4—7241no—
358C4—7241no—
359C4#1915386111yescharacteristic
360C4#1915386111yescharacteristic
361C2—41no—
362C2—81no—
363C2—14481no—
364C2#2604184611yescharacteristic
365C2#2604208711yescharacteristic
366C2#2604209411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#536×C181C2
socleC22×C181C22×D4
prime radical#26041424C2
hypercenter#536D181
hypocenterC181#3225
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26041900C2semidirect
2. #26041671C2semidirect
3. #26041661C2semidirect
4. #26041638C2semidirect
5. #26041629C2semidirect
6. #26041498C2semidirect
7. #26041491C2semidirect
8. #26041486C2semidirect
9. #26041481C2semidirect
10. #26041441C2semidirect
11. #26041435C2semidirect
13. #26041418C2semidirect
14. #26041340C2semidirect
15. #536×C181C2semidirect
183. C181#3225semidirect
186. #536D181semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260419002
#260416712
#260416612
#260416382
#260416292
#260414982
#260414912
#260414862
#260414812
#260414412
#260414352
#260414242
#260414182
#260413402
#536×C1812
#3225181